Just 11 weeks removed from a sweeping re-election victory, President Barack Obama has hit the ground running with an ambitious second-term agenda that includes tackling the mounting national debt, immigration and gun control.

But the window in which the president has any hopes of meeting his aggressive goals has already begun to close.

Confronting the fading effectiveness of a second-term presidency, dogged opposition from Republicans in Congress and unexpected hurdles that will inevitably arise over the next four years, Obama must act with a sense of urgency on his plans, particularly amid the fiscal cliff negotiations.

“Second-term presidents generally get eight months or so ... where there's a honeymoon to push an agenda,” said James Thurber, the director of Center for Congressional and Presidential Studies at American University. “He doesn't even have a month.”

Newly armed with “Organizing for Action” – the remnants of the president’s campaign structure, converted to a nonprofit for advocacy purposes – Obama has suggested he will indeed act quickly on his top priorities.

NBC News presidential historian Michael Beschloss points out that the US needs a president who is also going to suggest things that are not raised by an event of national magnitude, and that was something we saw a lot of in Obama's speech Monday.

But the next few months might well test the limits of the political capital that the president won in November, which saw Obama score a decisive victory over Republican opponent Mitt Romney and Democrats add seats in the House and the Senate.

If this past December’s lame duck Congress – in which Obama won higher tax rates for the wealthy, but only after a bitter fight with Republicans – offers any lessons, it’s that the GOP is equally committed to pursuing its own priorities, making compromise just as elusive as before.

The fiscal cliff fight will extend into this spring, when the government hits a series of major deadlines to keep the government funded and prevent a default on the national debt. That bare-knuckled fight could make or break Obama’s hopes of accomplishing much else on his agenda.

“I don't believe that he can wait until the last minute to deal with the debt ceiling and sequestration,” said Martin Frost, a former Democratic congressman from Texas. “That's got to be worked out during February.”

That fight would threaten to consume much of the political oxygen in Washington in any normal year. And Obama’s ability to pivot toward his other major priorities, gun violence and immigration, may well hinge upon how quickly and cleanly he can dispense with this spring’s spending fight.

TODAY's Lester Holt reports from Washington D.C. on how the struggles and victories of President Obama's first term have set the stage for opportunities of the second.

History suggests that many presidents cannot hope to accomplish much in the last two years of their term, when the jockeying for the next presidential campaign begins. And with midterm elections looming in 2014, lawmakers will inevitably turn at some point from governing to politicking.

"There's kind of an arc of achievement in presidential administrations. Usually the first few months of a new administration is where most of the accomplishment takes place," said Ross Baker, a presidential historian at Rutgers University. "It's hard to imagine getting another piece of legislation of the magnitude of the Affordable Care Act in the second term."

And Obama’s hopes of significant reforms to immigration and gun laws might well depend upon how well (or how poorly) the spending fight with Congress proceeds.

The president last week laid out a series of measures intended to curb gun violence, most significantly proposals to limit the size of ammunition magazines, ban assault weapons and require universal background checks on firearm purchases. That plan won little praise from Republicans, and Obama might have to lean upon any reservoir of goodwill he has left after the spending fight to reach his goals.

Obama is practically obligated to attempt immigration reform after soothing the Latino community during last year’s election about his inability to follow through with a pledge to accomplish immigration reform in his first term. If re-elected, Obama told Hispanic voters, he would make immigration reform a priority in this second term.

Both proposals could engender significant Republican resistance, a phenomenon familiar to any observers of Obama’s first four years in office.

Another significant – and unpredictable – variable that could ruin even the best-laid plans involves the unknown crises that will inevitably arise during Obama’s second term.

The "Meet the Press" moderator looks ahead to Monday's inaugural address, predicting President Obama will discuss economic relief and how he'll tackle America's toughest issues in a divided political atmosphere that's still "toxic" for the White House.

A foreign policy crisis could always erupt and consume the president’s attention. Uprisings in Egypt, Libya and Syria, for instance, proved to major developments during Obama’s first four years in office.

If anything, the president’s first term offered a cautionary tale of how difficult it can be to navigate the obstacles to success that can arise.

The president nearly saw his signature health reform law go down to defeat after the advent of the Tea Party movement, for instance.

And external events – a near-meltdown of the economy, mass shootings, the Gulf of Mexico oil spill and other crises – consumed as much of the president’s first term as anything else.

Just as foreign policy could prove to be a diversion from policy making, it’s one of the few policy areas where a lame-duck president can leave a legacy.

For instance, Bill Clinton, in the waning days of his presidency, concentrated on achieving an elusive peace deal between Israelis and Palestinians.

“He's got a whole range of things on his plate right now,” Frost said of Obama, “it just really depends on how he prioritizes things.”